Secondary Instabilities in Breaking Inertia–Gravity Waves

2012 ◽  
Vol 69 (1) ◽  
pp. 303-322 ◽  
Author(s):  
Mark D. Fruman ◽  
Ulrich Achatz
Keyword(s):  
Normal Mode ◽  
Gravity Waves ◽  
Singular Vector ◽  
Initial Conditions ◽  
Velocity Shear ◽  
Time Dependent ◽  
Unstable Wave ◽  
Singular Vectors ◽  
Secondary Instabilities ◽  
Inertia Gravity Waves

Abstract The three-dimensionalization of turbulence in the breaking of nearly vertically propagating inertia–gravity waves is investigated numerically using singular vector analysis applied to the Boussinesq equations linearized about three two-dimensional time-dependent basic states obtained from nonlinear simulations of breaking waves: a statically unstable wave perturbed by its leading transverse normal mode, the same wave perturbed by its leading parallel normal mode, and a statically stable wave perturbed by a leading transverse singular vector. The secondary instabilities grow through interaction with the buoyancy gradient and velocity shear in the basic state. Which growth mechanism predominates depends on the time-dependent structure of the basic state and the wavelength of the secondary perturbation. The singular vectors are compared to integrations of the linear model using random initial conditions, and the leading few singular vectors are found to be representative of the structures that emerge in the randomly initialized integrations. A main result is that the length scales of the leading secondary instabilities are an order of magnitude smaller than the wavelength of the initial wave, suggesting that the essential dynamics of the breaking might be captured by tractable nonlinear three-dimensional simulations in a relatively small triply periodic domain.

Inertia–Gravity Waves Generated within a Dipole Vortex

2007 ◽  
Vol 64 (12) ◽  
pp. 4417-4431 ◽  
Author(s):  
Chris Snyder ◽  
David J. Muraki ◽  
Riwal Plougonven ◽  
Fuqing Zhang
Keyword(s):  
Gravity Waves ◽  
Initial Conditions ◽  
Initial Period ◽  
Potential Temperature ◽  
Leading Edge ◽  
Vertical Shear ◽  
Coriolis Parameter ◽  
Dipole Vortex ◽  
The Waves ◽  
Inertia Gravity Waves

Abstract Vortex dipoles provide a simple representation of localized atmospheric jets. Numerical simulations of a synoptic-scale dipole in surface potential temperature are considered in a rotating, stratified fluid with approximately uniform potential vorticity. Following an initial period of adjustment, the dipole propagates along a slightly curved trajectory at a nearly steady rate and with a nearly fixed structure for more than 50 days. Downstream from the jet maximum, the flow also contains smaller-scale, upward-propagating inertia–gravity waves that are embedded within and stationary relative to the dipole. The waves form elongated bows along the leading edge of the dipole. Consistent with propagation in horizontal deformation and vertical shear, the waves’ horizontal scale shrinks and the vertical slope varies as they approach the leading stagnation point in the dipole’s flow. Because the waves persist for tens of days despite explicit dissipation in the numerical model that would otherwise damp the waves on a time scale of a few hours, they must be inherent features of the dipole itself, rather than remnants of imbalances in the initial conditions. The wave amplitude varies with the strength of the dipole, with waves becoming obvious once the maximum vertical vorticity in the dipole is roughly half the Coriolis parameter. Possible mechanisms for the wave generation are spontaneous wave emission and the instability of the underlying balanced dipole.

scholarly journals Exponential Smallness of Inertia–Gravity Wave Generation at Small Rossby Number

2008 ◽  
Vol 65 (5) ◽  
pp. 1622-1637 ◽  
Author(s):  
J. Vanneste
Keyword(s):  
Gravity Wave ◽  
Gravity Waves ◽  
Initial Conditions ◽  
Wave Generation ◽  
Rossby Number ◽  
Spontaneous Generation ◽  
Steady Flows ◽  
Generation Mechanisms ◽  
Inertia Gravity Waves ◽  
Exponentially Small

Abstract This paper discusses some of the mechanisms whereby fast inertia–gravity waves can be generated spontaneously by slow, balanced atmospheric and oceanic flows. In the small Rossby number regime relevant to midlatitude dynamics, high-accuracy balanced models, which filter out inertia–gravity waves completely, can in principle describe the evolution of suitably initialized flows up to terms that are exponentially small in the Rossby number ɛ, that is, of the form exp(−α/ɛ) for some α > 0. This suggests that the mechanisms of inertia–gravity wave generation, which are not captured by these balanced models, are also exponentially weak. This has been confirmed by explicit analytical results obtained for a few highly simplified models. These results are reviewed, and some of the exponential-asymptotic techniques that have been used in their derivation are presented. Two types of mechanisms are examined: spontaneous-generation mechanisms, which generate exponentially small waves from perfectly balanced initial conditions, and unbalanced instability mechanisms, which amplify unbalanced initial perturbations of steady flows. The relevance of the results to realistic flows is discussed.

scholarly journals A study of the dynamical characteristics of inertia–gravity waves in the Antarctic mesosphere combining the PANSY radar and a non-hydrostatic general circulation model

2018 ◽  
Author(s):  
Ryosuke Shibuya ◽  
Kaoru Sato
Keyword(s):  
General Circulation Model ◽  
Gravity Waves ◽  
General Circulation ◽  
Initial Conditions ◽  
Circulation Model ◽  
Reanalysis Data ◽  
Wind Fields ◽  
High Latitude Region ◽  
The Antarctic ◽  
Inertia Gravity Waves

Abstract. The first long-term simulation using the high-top non-hydrostatic general circulation model (NICAM) was executed to analyze mesospheric gravity waves in the period from April to August in 2016. Successive runs lasting 7 days are performed using initial conditions from the MERRA reanalysis data with an overlap of 2 days between consecutive runs. The data for the analyses were compiled from the last 5 days of each run. The simulated wind fields were closely compared to the MERRA reanalysis data and to the observational data collected by a complete PANSY (Program of the Antarctic Syowa MST/IS Radar) radar system installed at Syowa Station (39.6° E 69.0° S). It is shown that the NICAM mesospheric wind fields are realistic, even though the amplitudes of the wind disturbances appear to be larger than the radar observations. The power spectrum of the meridional wind fluctuations at a height of 70 km has an isolated and broad peak at frequencies slightly lower than the inertial frequency, f, for latitudes from 30° S to 75° S, while another isolated peak is observed at frequencies of approximately 2π/8 h at latitudes from 78° S to 90° S. The spectrum of the vertical fluxes of the zonal momentum also has an isolated peak at frequencies slightly lower than f at latitudes from 30° S to 75° S at a height of 70 km. It is shown that these isolated peaks are primarily composed of gravity waves with horizontal wavelengths of more than 1000 km. The latitude–height structure of the momentum fluxes indicates that the isolated peaks at frequencies slightly lower than f originate from two branches of gravity wave propagation paths. It is thought that one branch originates from 75° S due to topographic gravity waves generated over the Antarctic Peninsula and its coast, while more than 80 % of the other branch originates from 45° S and includes contributions by non-orographic gravity waves. The existence of isolated peaks in the high-latitude region in the mesosphere is likely explained by the poleward propagation of quasi-inertia–gravity waves and by the accumulation of wave energies near the inertial frequency at each latitude.

Filtering inertia-gravity waves from the initial conditions of the linear shallow water equations

2007 ◽  
Vol 19 (3-4) ◽  
pp. 204-218 ◽  
Author(s):  
Alexander Barth ◽  
Jean-Marie Beckers ◽  
Aida Alvera-Azcárate ◽  
Robert H. Weisberg
Keyword(s):  
Shallow Water ◽  
Gravity Waves ◽  
Shallow Water Equations ◽  
Initial Conditions ◽  
Inertia Gravity Waves

scholarly journals Effect of an oscillating time-dependent pressure gradient on Dean flow: transient solution

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Basant K. Jha ◽  
Dauda Gambo
Keyword(s):  
Pressure Gradient ◽  
Initial Conditions ◽  
Fluid Velocity ◽  
Outer Cylinder ◽  
Time Dependent ◽  
Navier Stokes ◽  
Dean Flow ◽  
Continuity Equations ◽  
Riemann Sum ◽  
Flow Formation

Abstract Background Navier-Stokes and continuity equations are utilized to simulate fully developed laminar Dean flow with an oscillating time-dependent pressure gradient. These equations are solved analytically with the appropriate boundary and initial conditions in terms of Laplace domain and inverted to time domain using a numerical inversion technique known as Riemann-Sum Approximation (RSA). The flow is assumed to be triggered by the applied circumferential pressure gradient (azimuthal pressure gradient) and the oscillating time-dependent pressure gradient. The influence of the various flow parameters on the flow formation are depicted graphically. Comparisons with previously established result has been made as a limit case when the frequency of the oscillation is taken as 0 (ω = 0). Results It was revealed that maintaining the frequency of oscillation, the velocity and skin frictions can be made increasing functions of time. An increasing frequency of the oscillating time-dependent pressure gradient and relatively a small amount of time is desirable for a decreasing velocity and skin frictions. The fluid vorticity decreases with further distance towards the outer cylinder as time passes. Conclusion Findings confirm that increasing the frequency of oscillation weakens the fluid velocity and the drag on both walls of the cylinders.

Semi-Lagrangian exponential time-integration method for the shallow water equations on the cubed sphere grid

2020 ◽  
Vol 35 (6) ◽  
pp. 355-366
Author(s):  
Vladimir V. Shashkin ◽  
Gordey S. Goyman
Keyword(s):  
Shallow Water ◽  
Gravity Waves ◽  
Shallow Water Equations ◽  
Time Integration ◽  
Standard Test ◽  
Integration Scheme ◽  
Test Problems ◽  
Cubed Sphere ◽  
Lagrangian Scheme ◽  
Inertia Gravity Waves

AbstractThis paper proposes the combination of matrix exponential method with the semi-Lagrangian approach for the time integration of shallow water equations on the sphere. The second order accuracy of the developed scheme is shown. Exponential semi-Lagrangian scheme in the combination with spatial approximation on the cubed-sphere grid is verified using the standard test problems for shallow water models. The developed scheme is as good as the conventional semi-implicit semi-Lagrangian scheme in accuracy of slowly varying flow component reproduction and significantly better in the reproduction of the fast inertia-gravity waves. The accuracy of inertia-gravity waves reproduction is close to that of the explicit time-integration scheme. The computational efficiency of the proposed exponential semi-Lagrangian scheme is somewhat lower than the efficiency of semi-implicit semi-Lagrangian scheme, but significantly higher than the efficiency of explicit, semi-implicit, and exponential Eulerian schemes.

scholarly journals Time Dependent Lyotropic Chromonic Textures in Microfluidic Confinements

Crystals ◽  
2020 ◽  
Vol 11 (1) ◽  
pp. 35 ◽  
Author(s):  
Anshul Sharma ◽  
Irvine Lian Hao Ong ◽  
Anupam Sengupta
Keyword(s):  
Phase Transition ◽  
Aspect Ratio ◽  
Temporal Dynamics ◽  
Initial Conditions ◽  
Flow Behavior ◽  
Medical Diagnostics ◽  
Time Dependent ◽  
Disodium Cromoglycate ◽  
M Phase ◽  
Static Conditions

Nematic and columnar phases of lyotropic chromonic liquid crystals (LCLCs) have been long studied for their fundamental and applied prospects in material science and medical diagnostics. LCLC phases represent different self-assembled states of disc-shaped molecules, held together by noncovalent interactions that lead to highly sensitive concentration and temperature dependent properties. Yet, microscale insights into confined LCLCs, specifically in the context of confinement geometry and surface properties, are lacking. Here, we report the emergence of time dependent textures in static disodium cromoglycate (DSCG) solutions, confined in PDMS-based microfluidic devices. We use a combination of soft lithography, surface characterization, and polarized optical imaging to generate and analyze the confinement-induced LCLC textures and demonstrate that over time, herringbone and spherulite textures emerge due to spontaneous nematic (N) to columnar M-phase transition, propagating from the LCLC-PDMS interface into the LCLC bulk. By varying the confinement geometry, anchoring conditions, and the initial DSCG concentration, we can systematically tune the temporal dynamics of the N- to M-phase transition and textural behavior of the confined LCLC. Overall, the time taken to change from nematic to the characteristic M-phase textures decreased as the confinement aspect ratio (width/depth) increased. For a given aspect ratio, the transition to the M-phase was generally faster in degenerate planar confinements, relative to the transition in homeotropic confinements. Since the static molecular states register the initial conditions for LC flows, the time dependent textures reported here suggest that the surface and confinement effects—even under static conditions—could be central in understanding the flow behavior of LCLCs and the associated transport properties of this versatile material.

Spontaneous-adjustment emission of inertia-gravity waves by unsteady vortical motion in the hurricane core

2010 ◽  
Vol 136 (647) ◽  
pp. 537-548 ◽  
Author(s):  
E. A. Hendricks ◽  
W. H. Schubert ◽  
S. R. Fulton ◽  
B. D. McNoldy
Keyword(s):  
Gravity Waves ◽  
Vortical Motion ◽  
Inertia Gravity Waves
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